The only force acting on the ball is gravity, so the net force is $F_{net} = -mg$ (taking upward as the positive direction). The impulse-momentum theorem is $F_{net} t = \Delta p = m(v_f - v_i)$. The initial velocity is $v_i = 10$ m/s, and the final velocity is $v_f = -20$ m/s.

$$-mgt = m(v_f - v_i)$$ $$t = \frac{v_f - v_i}{-g} = \frac{-20 \text{ m/s} - 10 \text{ m/s}}{-9.8 \text{ m/s}^2}$$